This tutorial is an introduction to the field of Performance Evaluation, with applications
to problems concerning the Quality of Service in the Internet, and communication
networks in general. The tutorial will first review the basic mathematical tools
and results used in the modeling of telecommunication systems: stochastic processes,
Markov Chains, and the theory of queues. Then, as illustrations and applications,
we will detail models of several algorithms or protocols used in networks: routing
algorithms; flow control mechanisms, including TCP; mechanisms for service differentiation,
including IntServ and DiffServ.

Alain Jean-Marie received the Matrise Es-Sciences in Mathematics,
and the Doctorat de 3me cycle, from the University of Paris XI at Orsay, in 1985
and 1987 respectively. During 1988-89, he was a Post-Doctoral fellow at the University
of Maryland. From 1987 to 1999, he has been a member of the performance evaluation
group at INRIA, Sophia Antipolis, France. He is now professor at the University
of Montpellier, France. His research interests include modeling and performance
evaluation for real-time systems and communication networks, control theory, analysis
of algorithms and parallel computing.